Notitie
Princetonlaan 6
3584 CB Utrecht
P.O. Box 80015
3508 TA Utrecht
The Netherlands
www.tno.nl
From
D. Maljers, J.H. ten Veen, M. den Dulk
T +31 88 866 42 56
F +31 88 866 44 75
Subject
Description Uncertainty procedure DGM-deep
Date
4 March 2015
Our reference
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1.
Introduction to Uncertainty modelling
The DGM-deep model provides the end-user with a regional subsurface layer
model that represents the onshore geological structures of the Netherlands.
Although the 250 m resolution of the model prohibits decision making on a very
small scale, e.g. for hydrocarbon reservoirs studies, it is widely used by variety of
end users to support policy making. In order to assess the usability and reliability
of the DGM-deep model, a measure for the uncertainty is provided.
In statistics, generally 2 types of uncertainties or errors are discriminated, i.e.
accuracy and precision, as is illustrated in Figure 1A. Whereas, accuracy reflects
the proximity of a model results to the true value; precision gives information on
the reproducibility of the model results, neglecting the accuracy of the underlying
input data. Stochastic modelling, in which multiple realizations for each horizon are
generated, produces a Standard Deviation that gives information on probability of
the model. Residual grids on the other hand could be relevant in view of accuracy
since they reflect the correctness of the model at the well location. In the
uncertainty workflow applied, accuracy and precision are combined. This is
achieved by using the residual grids in the well-tie process, such that standard
deviations between the well locations are centered around the well-tied depths
surfaces (Figure 1B). This process does not addresses the source of misties at
well location; this is subject of further research.
Figure 1 A) Accuracy is the proximity of measurement results to the true value; precision, the
repeatability, or reproducibility of the measurement. B) Combined accuracy-precision workflow
applied to DGM-deep.
E-mail
[email protected]
Direct dialling
+31 88 866 45 32
Date
4 March 2015
2.
Stochastic uncertainty modeling
In order to present a measure for the probability of the depth of the modelled
layers, we developed a stochastic uncertainty workflow. This workflow consists of
building time maps for each horizon from seismic interpretations that are
subsequently converted to the depth domain using an acoustic velocity model
(VELMOD-3), taking into account the potential error bandwidth for each data
source. A stochastic simulation algorithm (Sequential Gaussian Simulation, SGS)
is applied in order to generate multiple random realizations for each horizon, both
in time and depth domain.
The workflow takes into account the following three error sources:
 Data error: This error takes into account any error related to the picking of a
horizon within a seismic dataset and includes processing errors, vertical
shifting errors and resolution errors. The data error increases with depth due
to decreasing quality of the seismic data. Also a larger error has been
assumed for picks traced from 2D seismic than those from 3D seismic. The
data error is added as a noise factor to the original horizon picks using a short
correlation distance (<1 km). Each realization is conditioned to the available
data but varies within the error bandwidth away from the points.
 Structural complexity: Areas characterized by low structural complexity will
produce small errors with interpolation, while in structurally complex areas a
larger error is introduced. Therefore, structural complexity importantly affects
the uncertainty. At the location of data points, the depth values will range
within the data error bandwidth. Moving away from data points, the error
gradually increases up to the maximum interpolation error set by the regionally
varying structural error.
 Velocity model error: For each map of V0, a set of SGS realizations has been
calculated using the same interpolation and variogram settings as used in the
VELMOD-3 model.
Finally, the errors are combined to a joint depth error following these steps (
Figure 2):
A random depth-dependent data error is added to all seismic horizon
picks.
A random realization of a set of time domain maps for each horizon is
obtained from the SGS interpolation of the seismic horizon picks (plus
error) in combination with regional structural error maps.
A random realization of V0 maps for each horizon is obtained from SGS
interpolation of all available well velocity determinations and variogram
and interpolation parameters from VELMOD-3.
A random realization of a set of depth domain maps is obtained from timedepth conversion of the realized time maps using the realized V0 maps.
Kriging interpolation of residual well marker mismatches and the
subsequent correction for these residuals ensures that the maps are
conditioned to the wells used.
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Calculation of SD from the multiple realizations of the final depth maps .
Date
4 March 2015
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Figure 2 Workflow used to calculate the uncertainties. See text for further explanation.
3.
How to use the uncertainty depth maps?
Uncertainties are represented as standard deviations, i.e. a statistical measure for
the spread of values, in this case the SD of two way travel time (TWT) and true
vertical depth (TVD). The provided DGM-deep depth map represents the best
estimate of the base of a unit. However, the true base of the unit may be
positioned shallower or deeper. The likelihood that the real depth value lies
between the estimated value plus or minus 1 times the standard deviation is ca
64%. For a range of 2 times the standard deviation the likelihood is ca 95%. For a
specific location, it can be said that the base of the unit, with 5% uncertainty, lies
between the minimum and maximum. The width of the confidence interval differs
for each location as it is depending upon the SD (Figure 3). Therefore, end-users
that apply the mean/estimated depth map for further purposes should realize that
not a single confidence value can be attached to this specific depth map, only that
it is in the middle of a 95% confidence interval and therefore considered the best
pick.
Figure 3 shows a cross section of the depth of the North Sea Group, the 95%
confidence interval and 4 equally likely realizations out of 500 of this depth. Along
the cross section, the variation in SD values (and thus the width of the 95%
confidence interval) clearly stand out. For example, between 20.000 and 30.000
m a region with a low SD is visible that corresponds to a region with 3D seismic
data coverage. From 30.000 m onwards, the SD dramatically increases. This part
of the cross section crosses the Ruhr Valley Graben, a structurally complex area,
where only 2D seismic data are available.
Date
4 March 2015
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Depth [m]
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Distance [m]
Figure 3 Cross section; bold black line: mean of 500 realizations of the depth of the North Sea
Group; dotted black lines: 95% confidence interval; colored lines: individual realizations (4 out of
500). Map shows the SD of the depth of the North Sea Group (light blue: low SD, dark blue: high
SD) and the position of the cross section.
4.
Drawbacks of the uncertainty method
The uncertainty workflow applied is an effective way to represent the reliability of
the model, but since it is built upon various error sources, the relative contribution
of these individual sources may need further explanation.
For instance, data proximity appears to have more impact on the standard
deviation than structural complexity and depth. This is well exemplified by the
depth of the base Triassic in the West Netherlands Basin. This depth surface has
a relatively low SD, even though a high standard deviation is expected based on
the high structural complexity of the area. This shows that for areas covered by 3D
seismic the SD may erroneously suggest a high reliability.
If for the same area well depths are considered as true depths, the mistie values,
in a sense, reflect the reliability of the model at the well location. “In a sense”
because extraction of mistie values and resulting residual grids are part of a
deterministic approach that yields a measure for accuracy but not for precision as
does the stochastic approach (see Figure 1).
Date
4 March 2015
Comparison of residual grids and standard deviation (SD), e.g. in the same area in
the West Netherlands Basin, show that the low standard deviation correspond with
large residuals. Thus, the large residuals in these areas provide additional and
better information on the overall reliability of the model.
In general residual grids show large residual values in older stratigraphic intervals
(CK-RB). Large residual values are furthermore observed in areas with strong
variable relief such as near faults or near salt domes. Often when large residuals
are observed the misties value are related to a strong relief in combination with a
lack in model detail. An easy solution through local correction may be applicable
without severely distorting the initial surface trend. If this solution were to be
applied the residual grid will show a local severe peak at the well location. If a
local correction is not acceptable the solution is much more complex. Every step
in the modeling workflow, from the interpretation phase to the end product in depth
may contribute to these large residual values and preferably every step needs reevaluation, which is a time-consuming process.
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